# Can you solve my Chess Sudoku puzzles?

### Rules

• Normal Sudoku rules apply except that instead of 9s you must place chess pieces. A puzzle can mix chess pieces, and in principle any piece may be used - although the rest of the constraints provide implicit limitations on which pieces may go in which squares.
• Each chess piece attacks each number from 1 to 8 precisely once.
• Attacks "pass though" numbers - see the Bishops in the second puzzle.
• Chess pieces do not attack (or protect) other chess pieces.

The space of possible puzzles is very small, and most of them are very symmetric, which makes them less interesting. Therefore I am posting two puzzles, not one: these are essentially the two distinct representatives of interesting chess Sudoku puzzles.

## Puzzle 2

• Can we put any kind of chess piece, or is the first puzzle only Kings and the second only Bishops? Dec 24, 2014 at 11:40
• @McMagister, you can mix them. I've updated the question to make this clear. Dec 24, 2014 at 11:42
• I'd like to contact you for publishing these. Could you contact me? -- Ed Pegg Jr Jul 16, 2017 at 13:19

The solution for the first puzzle is:

That was very interesting, I have to say. Here are the things that helped the most:

• Rooks and queens attack too many squares, while pawns attack too little. Hence all 9s are either knights, bishops or kings.
• To attack 8 squares, knights and kings must be in the interior somewhere. Hence any 9 on the edge is a bishop (this is the single fact that helped the most!)
• Assume a square is a 9 and a certain chess piece. If there is a doubled up number in the 8 squares attacked by that piece, then that piece can't go there. If no pieces can go there, then it can't be a 9.
• If you know what and where some of the pieces are, then you can look at the attacked squares. For example, if you have a square where an 8 could go under normal Sudoku rules, but is being attacked by a bishop that's already attacking an 8, then 8 can't go there.

Someone else can do the other one :) (It's good fun!)

• Nice observations about which pieces can be used! Dec 25, 2014 at 19:37
• Any solution for Knights? Dec 26, 2014 at 19:18
• It's worth noting that it's possible for a rook or queen to be used by interposing other pieces. A simple example would be a rook on square A1, any other piece on square A3 and no other piece on the first rank. The rook attacks the other seven squares on the first rank, and the A2 square. Whether this is useful for either of these puzzles, I don't know. Apr 10, 2015 at 14:15
• @Tetrinity - Except the directions explicitly stated that no chess piece can attack any other chess piece. And also that would be the equivalent of having two 9's in the same row, something that wouldn't work in regular Sudoku rules either. Apr 19, 2016 at 14:28

Over a year late, but here's the second puzzle's solution, painstakingly drawn in MS Paint:

A little disappointed neither of them involved any knights. That would've made for an even more interesting challenge.

• As a slight generalisation of your comment, IMO it's disappointing how few distinct boards there are which meet the rules. Apr 20, 2016 at 21:45
• @PeterTaylor - Indeed - the positions of the chess pieces in this one appears to be a simple mirror image of the first. Are you saying there are no valid solutions involving knights? Or with bishops in the corner boxes maybe? I've never made a Sudoku before, only solved them, so not sure how you go about making sure it has only one solution, etc. Apr 21, 2016 at 13:33
• I am indeed saying that there are no valid solutions involving knights. I started by generating all full boards which meet the criteria, using Knuth's "dancing links" algorithm, and then I generated the puzzles by repeatedly clearing cells which could be filled in by reasoning from the remaining cells. Apr 21, 2016 at 13:46